import math
from math import *
def _1():
    length = eval(input("Enter the length from the center to a vertex:"))
    side = 2 * length * sin(pi / 5)
    print("The area of the pentagon is",5 * side * side / (4 * tan(pi / 5)))


def _2():
    lat1, lon1 = eval(input("Enter point 1 (latitude and longitude) in degrees:"))
    lat2, lon2 = eval(input("Enter point 2 (latitude and longitude) in degrees:"))
    x1 = radians(lat1)
    x2 = radians(lat2)
    y1 = radians(lon1)
    y2 = radians(lon2)
    print("The distance between the points is", 6371.01*acos(sin(x1)*sin(x2)+cos(x1)*cos(x2)*cos(y1-y2)))
    

def _3():
    pass


def _4():
    side = eval(input("Enter the side:"))
    print("The area of the pentagon is",(5*side**2)/(4*tan(pi/5)))


def _5():
    sides = eval(input("Enter the number of sides"))
    side = eval(input("Enter the side:"))
    print("The area of the polygon is",(sides*side**2)/(4*tan(pi/sides)))


def _6():
    pass

def _7():
    pass